哈肯定理的唯一性

IF 0.8 3区数学 Q2 MATHEMATICS

Michigan Mathematical Journal Pub Date : 2020-04-15 DOI:10.1307/mmj/20216081

M. Freedman, M. Scharlemann

{"title":"哈肯定理的唯一性","authors":"M. Freedman, M. Scharlemann","doi":"10.1307/mmj/20216081","DOIUrl":null,"url":null,"abstract":"Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk S in a Heegaard split manifold M in which every sphere separates, the Heegaard surface T can be isotoped so that it intersects S in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel S 2) pushing a stabilizing pair of T through S and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Uniqueness in Haken’s Theorem\",\"authors\":\"M. Freedman, M. Scharlemann\",\"doi\":\"10.1307/mmj/20216081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk S in a Heegaard split manifold M in which every sphere separates, the Heegaard surface T can be isotoped so that it intersects S in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel S 2) pushing a stabilizing pair of T through S and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group.\",\"PeriodicalId\":49820,\"journal\":{\"name\":\"Michigan Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2020-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Michigan Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1307/mmj/20216081\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Michigan Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1307/mmj/20216081","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

继Haken和Casson-Gordon之后，在[Sc]中表明，给定Heegaard分裂流形M中每个球体分离的还原球或边界还原盘S, Heegaard曲面T可以被同位素化，使其与S相交成一个圆。在这里，我们表明，当T的两个不同位置实现这一目标时，一个可以通过一系列的方式移动到另一个:1)T的同位素S, 2)推动稳定的T对通过S, 3) T的眼镜状扭曲。最后一个移动的灵感来自鲍威尔提出的Goeritz组的发电机之一。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Uniqueness in Haken’s Theorem

Following Haken and Casson-Gordon, it was shown in [Sc] that given a reducing sphere or boundary-reducing disk S in a Heegaard split manifold M in which every sphere separates, the Heegaard surface T can be isotoped so that it intersects S in a single circle. Here we show that when this is achieved by two different positionings of T, one can be moved to the other by a sequence of 1) isotopies of T rel S 2) pushing a stabilizing pair of T through S and 3) eyegelass twists of T. The last move is inspired by one of Powell's proposed generators for the Goeritz group.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Michigan Mathematical Journal 数学-数学

CiteScore

1.20

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Michigan Mathematical Journal is available electronically through the Project Euclid web site. The electronic version is available free to all paid subscribers. The Journal must receive from institutional subscribers a list of Internet Protocol Addresses in order for members of their institutions to have access to the online version of the Journal.